Three-webs with covariantly constant curvature and torsion tensors

In this paper, we study a special class of multidimensional 3-webs with covariantly constant curvature and torsion tensors. In the first part, we prove that 3-webs of the class belong to $G$-webs, i.e., there is a subfamily of adapted frames whose components of curvature and torsion tensors are constant. The structure of homogeneous space $G/H$ carrying the 3-web is described. Structure equations of $G$-group are found. In the second part, we have found structure equations of $W^\nabla$-web and finite equations of some special web classes.